A robust hybrid exponentially weighted moving average chart for monitoring time between events

Monitoring time between events (TBE) is an essential aspect of the high-yield processes where the events of interest rarely occur. This study proposes a one-sided scheme of a hybrid exponentially weighted moving average (HEWMA) chart for monitoring TBE, where it is assumed that the TBE observations follow a gamma distribution. This chart is symbolized as the HEWMATBE chart. The HEWMATBE chart detects the downward shift, that is, a decrease in the interarrival times that can lead to a deterioration of the process. A simulation study is carried out for the numerical results, and one-sided HEWMATBE chart is evaluated along with one-sided triple EWMA (TEWMATBE), double EWMA(DEWMATBE), EWMA(EWMATBE), double GWMA(DGWMATBE), and GWMA(GWMATBE) charts. The results show that the one-sided HEWMATBE chart outperforms its rivals, particularly in the case of small-to-moderate downward shifts. Moreover, this study also investigated the robustness of the HEWMATBE chart, where the true distribution of the TBE observations is assumed to be Weibull or lognormal, and it is found that the HEWMATBE chart is reasonably robust. Finally, two examples are given to demonstrate how to use the HEWMATBE chart in real-world situations.